Brian W. Rogers

Homophily and Long-Run Integration in Social Networks

We model network formation when heterogeneous nodes enter sequentially and form connections through both random meetings and network-based search, but with type-dependent biases. We show that there is “long-run integration”, whereby the composition of types in sufficiently old nodesʼ neighborhoods approaches the global type-distribution, provided that the network-based search is unbiased. However, younger nodesʼ connections still reflect the biased meetings process. We derive the type-based degree distributions and group-level homophily patterns when there are two types and location-based biases. Finally, we illustrate aspects of the model with an empirical application to data on citations in physics journals.

Relating Network Structure to Diffusion Properties through Stochastic Dominance

We examine the spread of a disease or behavior through a social network. In particular, we analyze how infection rates depend on the distribution of degrees (numbers of links) among the nodes in the network. We introduce new techniques using first- and second order stochastic dominance relationships of the degree distribution in order to compare infection rates across different social networks.

Diversity and Popularity in Social Networks

Homophily, the tendency of linked agents to have similar characteristics, is an important feature of social networks. We present a new model of network formation that allows the linking process to depend on individuals types and study the impact of such a bias on the network structure. Our main results fall into three categories: (i) we compare the distributions of intra- and inter-group links in terms of stochastic dominance, (ii) we show how, at the group level, homophily depends on the groups size and the details of the formation process, and (iii) we understand precisely the determinants of local homophily at the individual level. Especially, we find that popular individuals have more diverse networks. Our results are supported empirically in the AddHealth data looking at networks of social connections between boys and girls.

Symmetric Play in Repeated Allocation Games

We study symmetric play in a class of repeated games when players are patient. We show that, while the use of symmetric strategy profiles essentially does not restrict the set of feasible payoffs, the set of equilibrium payoffs is an interesting proper subset of the feasible and individually rational set. We also provide a theory of how rational individuals play these games, identifying particular strategies as focal through the considerations of Pareto optimality and simplicity. We report experiments that support many aspects of this theory.

Diffusion and protection across a random graph

We study the interplay between the diffusion of a harmful state in a network of contacts and the possibility of individual agents to undertake costly investment to protect themselves against infection. We characterize how equilibrium diffusion outcomes, such as the immunization rate, total prevalence and welfare, respond to changes in the architecture of the network, and show that these responses depend on the details of the diffusion process.

A comment on “Egalitarianism and efficiency in repeated symmetric games” by V. Bhaskar [Games Econ. Behav. 32 (2000) 247–262]☆

Abstract We identify an error in Bhaskarʼs (2000) Proposition 4. We provide counterexamples to this result and demonstrate that it is not correctable.

An Incomplete Information Justification of Symmetric Equilibrium in Symmetric Games

Consider a symmetric 2-player game of complete information. Consider an arbitrary Bayesian extension of that game with payoff-irrelevant types, independent random matching, and anonymity (private types). We show that, in this setting, while strategies in a Bayesian Nash equilibrium of that game can differ across types, aggregate play in any such equilibrium must coincide with a symmetric Nash equilibrium of the complete information game. This justifies the interpretation of certain data, including many laboratory experiments, as arising from a symmetric equilibrium, even when asymmetric equilibria exist and, in addition, subjects may be heterogeneous.

Cooperation, punishment and immigration

We study the incentive to cooperate in a society comprised of citizens and immigrants. The level of cooperation is governed by a steady state under population dynamics, along with the behavior of individual citizens and immigrants. We provide an equilibrium characterization, exhibiting a uniquely determined positive level of cooperation in society. We then use this framework to study the impact of government programs aimed at punishing immigrants who defect. When agents produce offspring, we show that a consequence of such punishment is that, while the incentive for immigrants to defect decreases, there is an equilibrium substitution effect whereby citizens realize an increased incentive to defect.